Sonic modulus

Modulus The ratio of stress to strain in a material over the range for which this value is constant. The type of modulus, which is measured, depends on the method of measurement, e.g., dynamic modulus, compressive modulus, elastic or tensile (Young s) modulus, shear modulus, torsion modulus, sonic modulus. 

The sonic modulus sonic and the X-ray data for sin S were fitted on the assumption that PPTA fibres can be considered an aggregate of small crystals (similar to chain-extended polyethylene discussed above). We have... 

The function N(0)=p(0)sin0 is proportional to the total number of domains in the fibre at an angle 0 with the fibre axis. The determination of the modulus using sonic frequencies will yield a higher value of g than the method by which the modulus is derived from the initial slope of the tensile curve. For random orientation of the chains in a fibre (sin20),=O.5 and the modulus of an isotropic fibre is given by Eiso 4g. 

Fig. 53 The sonic modulus as a function of the number-average molecular weight for a series of experimental PpPTA yarns with different molecular weights specified in Table 4...

Table 4 The molecular weight, sonic modulus and strength of experimental PpPTA yarns. The molecular weight of a single monomer is 238... 

For crb 0 the lifetime fb °°,so Eq. 115 presents a non-linear relation between log( b) and the creep stress crb, which is different from the Coleman relation. According to Eq. 115, at constant load the lifetime of a fibre decreases with increasing orientation parameter. Figure 61 compares the observed data for a PpPTA fibre by Wu et al. with the calculated lifetime curve using the parameter values /J=0.08, tan =0.1483, g= 1.6 GPa, j O.032 (GPa)-1, which implies a fibre with a sonic modulus of 91.8 GPa [30]. As shown by Wu et al., fibres that were tested at high stresses had shorter lifetimes than those calculated from the experimental lifetime relation. 

Young s modulus for various materials measured with Grindo-Sonic... 

Seebeck sclerometer, 48 Shear modulus, 9 Shore sclerometer, 118 Sonic Mill method, 39 Strain tensor, 11 Stress tensor, 11... 

Fig. 9.13. Hardness estimation of materials through Young s modulus measured with Grindo-Sonic. (After Jakubicki et al., 1979). Numbers as in Table 9.4.

Sonic Modulus. If crack or craze branching is the operative mech-nism in toughening, toughness should be directly related to the difference in sonic speeds in matrix and dispersed phases. Experiments to confirm this effect were undertaken using three commercial ABS resins. These were selected to represent the three main rubber types encountered commercially an acrylonitrile/butadiene copolymer rubber, a butadiene rubber with grafted styrene/acrylonitrile copolymer, and a block polymer of... 

Aksel, C. and Riley, F.L., Young s modulus measurements of magnesia-spinel composites using load-deflection curves, sonic modulus, strain gauges and Rayleigh waves , J. Eur. Ceram. Soc., 2003 23(16) 3089-96. 

Notwithstanding this great variety of mechanical properties the deformation curves of fibres of linear polymers in the glassy state show a great similarity. Typical stress-strain curves of poly(ethylene terephthalate) (PET), cellulose II and poly(p-phenylene terephtha-lamide (PpPTA) are shown in Fig. 13.89. All curves consist of a nearly straight section up to the yield strain between 0.5 and 2.5%, a short yield range characterised by a decrease of the slope, followed by a more or less concave section almost up to fracture. Also the sonic modulus versus strain curves of these fibres are very similar (see Fig. 13.90). Apart from a small shoulder below the yield point for the medium- or low-oriented fibres, the sonic modulus is an increasing, almost linear function of the strain. 

FIG. 13.90 Typical sonic modulus vs. strain curves of PET, cellulose II and PpPTA fibres. The differences in initial moduli per polymer are due to differences in orientation angles. From Northolt and Baltussen (2002). Courtesy John Wiley Sons, Inc. 

Ef is the sonic modulus of the fibre. From Eq. (13.167) it follows that measurement of and 0(relation between the compliance and the orientation parameter (sin20)E/[l+erF/(2gd)]- This relation has been verified experimentally by a combined sonic modulus-X-ray diffraction experiment on a PpPTA fibre (Baltussen and Northolt, 2002), as shown in Fig. 13.100. Linear regression yields eA = 240 GPa and gd = 1.60 GPa. 

Sonic absorption on the other hand is - for linear polymers - a typical constitutive property, dependent of temperature and frequency, for which no additivity techniques are available. For cross-linked polymers the integrated loss modulus-temperature function (the "loss area") in the glass-rubber transition zone shows additive properties. 

Reflectance, Moisture Regain, Sonic Modulus, and DTA, NBS Report 10687, NTIS, COM 75-10162, Feb. 1972. 

Infrared dichroism is one of numerous methods used to characterize molecular orientation. The degree of anisotropy of the strained pol3rmers may also be accurately characterized by other techniques such as X-ray diffraction, birefringence, sonic modulus, polarized fluorescence and polarized Raman spectroscopy [2]. These techniques directly probe the orientational behavior of macromolecular chains at a molecular level, in contrast to the macroscopic information provided by mechanical measurements. 

The sound velocity in a fiber, and the sonic modulus calculated therefrom, are related to molecular orientation (De Vries ). As shown by Moseley ), the sonic modulus is independent of the crystallinity at temperatures well below the T (which means that the inter- and intramolecular force constants controlling fiber stiffness are not measurably different for crystalline and amorphous regions at these temperatures). An orientation parameter a, calculated from the sonic modulus, is therefore taken as a measure for the average orientation of all molecules in the sample, regardless of the degree of crystallinity. The parameter is called the total orientation , as contrasted to crystalline and amorphous orientation, from X-ray data. 

The relationship between sonic modulus and sound velocity C is given by ... 

Anticipating experimental results reported in detail in Section 4, we present in Fig. 9a correlation of the sonic modulus of carbon fibers and that of their precursors. Included are a variety of copolymers and blends. (For identification of the samples see Table 11.) Although there is some scattering, the trend shows clearly that high molecular order in the precursor is certainly a desirable property. 

Fig. 9. Sonic modulus of carbon fibers as a function of the sonic modulus of the precursors ( standard screening conditions , cf. Table 11)...

The quality of the carbon fibers was evaluated mainly from the tensile properties, modulus E and tensile strength a. Sonic modulus was used instead of tensile modulus, because the method appeared to be more reliable. Apart from E, and a, the carbon fiber density q was determined. 

The importance of molecular orientation has been discussed in Section 3.4.1. In particular, the linear relationship between the sonic modulus of the carbon fiber and that of the precursor was exemplified in Fig. 9. 

Fig. 17 shows that the single filament tenacity (Instron) of the precursor may be considered as a suitable, simple indicator for molecular orientation. For a wide variety of precursor compositions, comonomer concentrations and spinning conditions, there is a relatively good linear relationship between sonic modulus and tenacity of the precursor fiber. The identification of the data points is given in Table 11. (Not all of the fibers used for Fig. 17 have been actually transformed to carbon fibers some of the AN/VBr carbon fiber data are taken from Sect. 5.)... 

It appears plausible to identify the extrapolated value of the modulus at tenacity zero as the sonic modulus of unoriented fiber , (cf. Eq. 22). This magnitude. 

Table 11. Sonic modulus and tenacity of precursor fibers, and sonic modulus of carbon fibers (where determined under standard stabilization conditions cf. Fig. 9).

The carbon fibers were characterized by their tensile strength a, sonic modulus E, and density q. 

Due to the low breaking load of the bundles, Instron tensile moduli were not sufficiently reliable. Modulus data were therefore obtained by the sonic technique, using a modified PPM-5 (H. H. Morgan Company) dynamic modulus tester (Murayama ). 

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